Group “Classical and Quantum Dynamical Systems”
The main research focus of the Quantum Dynamics and Spectral Analysis team is the mathematical study of problems arising in physics and their applications. Most of our activity concerns the spectral and scattering properties of models of nanostructures, models in atomic physics and particle physics in quantum field theory, the properties of solutions of the PDEs of physics, and the properties of uniqueness, stability, and reconstruction in inverse problems.
The main strengths of our scientific activity:
Nanostructures: Propagation properties of waves in optical fibers and quantum waveguides; spectral properties of differential operators on graphs; study of the semiconducting character and gap opening in graphene samples with periodic perforations.
PDEs and inverse problems: Convergence-to-equilibrium properties for dilute particle gases and regularization of solutions to the nonlinear Kac and Boltzmann equations; inverse problems in models of anomalous diffusion involving fractional-time equations (complex fluids, porous media, diffusion of pollutants in soil); inverse problems for characteristic coefficients (diffusion, absorption, etc.), with applications to waveguides, angiogenesis, Black–Scholes models, etc.
Standard Model, QFT and atomic physics: Rigorous analysis of Hamiltonians in particle physics: non-perturbative quantum electrodynamics; spectral theory for weak interaction models and muonic atoms; derivation of the Van der Waals–London laws; spectral theory in quantum field theory on de Sitter spaces and scattering theory on Lorentzian manifolds in QED; edge currents and surface states for magnetic Schrödinger operators.
| ALVAREZ | Benjamin | Research teacher | +33.4.91.26.97.92 | Contact |
| BARBAROUX | Jean-Marie | Research teacher Team leader « Quantum Dynamics and Spectral Analysis » | +33.4.91.26.95.03 | Contact |
| BRIET | Philippe | Research teacher | +33.4.91.26.95.11 | Contact |
| GOUTTENEGRE | Hugo | Ph.D. | Contact | |
| PANATI | Annalisa | Research teacher | +33.4.91.26.95.46 | Contact |
| PILLET | Claude-Alain | Research teacher | +33.4.91.26.95.32 | Contact |
| ROULEUX | Michel | Research teacher | +33.4.91.26.97.97 | Contact |
| SOCCORSI | Eric | Research teacher | +33.4.91.26.95.37 | Contact |
The second critical density and generalised condensation
Condensed Matter Physics, 2010, 13 (2), pp.23003. (10.5488/CMP.13.23003)
The semiclassical Maupertuis-Jacobi correspondence and applications to linear water wave theory
Matematicheskie Zametki / Mathematical Notes, 2010, 87 (3), pp.430-435. (10.1134/S0001434610030168)
Hydrogenic systems confined by infinite tubes
Journal of Physics A: Mathematical and Theoretical, 2010, 43 (47), pp.474018. (10.1088/1751-8113/43/47/474018)
Diamagnetism of quantum gases with singular potentials
Journal of Physics A: Mathematical and Theoretical, 2010, 43 (47), pp.474008. (10.1088/1751-8113/43/47/474008)
Poisson Statistics for Eigenvalues of Continuum Random Schrödinger Operators
Analysis & PDE, 2010, 3 (1), pp.49-80. (10.2140/apde.2010.3.49)
Sub-linear capacity scaling for multi-path channel models
Mathematical Methods in the Applied Sciences, 2010, 33 (9), pp.1164-1180
On the two-dimensional Coulomb-like potential with a central point interaction
Journal of Physics A: Mathematical and Theoretical, 2010, 43 (47), pp.474020. (10.1088/1751-8113/43/47/474020)
A partition-free approach to transient and steady-state charge currents
Journal of Physics A: Mathematical and Theoretical, 2010, 43 (47), pp.474011. (10.1088/1751-8113/43/47/474011)
Spectral and transport properties of quantum systems: in memory of Pierre Duclos (1948–2010) : PREFACE
Journal of Physics A: Mathematical and Theoretical, 2010, 43 (47), pp.470301. (10.1088/1751-8121/43/47/470301)
100 years of improvements of bounding properties of Padé approximants to the Stieltjes functions: One-point, two-point and N-point Padé approximants
Applied Numerical Mathematics: an IMACS journal, 2010, 60 (12), pp.1320-1331. (10.1016/j.apnum.2010.05.007)
